Paper Info

Title | ||
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On the rank of higher inclusion matrices. |

Abstract | ||
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Let r >= s >= 0 be integers and G be an r-graph. The higher inclusion matrix M-s(T)(G) is a {0, 1}-matrix with rows indexed by the edges of G and columns indexed by the subsets of V (G) of size s: the entry corresponding to an edge e and a subset S is 1 if S subset of e and 0 otherwise. Following a question of Frankl and Tokushige and a result of Keevash, we define the rank-extremal function rex(n, t, r, s) as the maximum number of edges of an r-graph G having rk M-s(T)(G) <= ((n)(s)) - t. For t at most linear in n, we determine this function as well as the extremal r-graphs. The special case t = 1 answers a question of Keevash. |

Year | DOI | Venue |
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2014 | 10.1112/jlms/jdu029 | JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES |

Field | DocType | Volume |

Row,Integer,Combinatorics,Matrix (mathematics),Mathematics,Special case | Journal | 90 |

Issue | ISSN | Citations |

2 | 0024-6107 | 0 |

PageRank | References | Authors |

0.34 | 3 | 3 |

Authors (3 rows)

Cited by (0 rows)

References (3 rows)

Name | Order | Citations | PageRank |
---|---|---|---|

Codrut Grosu | 1 | 1 | 2.09 |

Yury Person | 2 | 118 | 19.19 |

Tibor Szabó | 3 | 5 | 0.92 |